Fun with Fibonacci

We introduce a function which measures the number of distinct ways in which a number can be expressed as the sum of Fibonacci numbers. Using a binary table and other devices, we explore the values that can take and reveal some interesting patterns. The article shows how standard spreadsheet functionalities make it possible to reveal quite striking patterns in data, and is intended to be used in the classroom.

The slumbarumba jumbuck problem

The potential for simple linear relationships arising from a computer game to build student modelling and "world problem" skills is explored. The fundamental capability of the spreadsheet to tabulate and graph possible solutions is used to lay bare the problem structure for the students.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

Basic finance made accessible in Excel 2007 : "the big 5, plus 2"

The basic principles and equations are developed for elementary finance, based on the concept of compound interest. The five quantities of interest in such problems are present value, future value, amount of periodic payment, number of periods and the rate of interest per period. We consider three distinct means of computing each of these five quantities in Excel 2007: (i) use of algebraic equations, (ii) by recursive schedule and the Goal Seek facility, and (iii) use of Excel's intrinsic financial functions. The paper is intended to be used as the basis for a lesson plan and contains many examples and solved problems. Comment is made regarding the relative difficulty of each approach, and a prominent theme is the systematic use of more than one method to increase student understanding and build confidence in the answer obtained. Full instructions to build each type of model are given and a complete set of examples and solutions may be downloaded (Examples.xlsx and Solutions.xlsx).

Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

Revisiting Polya's summation techniques using a spreadsheet : from addition tables to Bernoulli polynomials

Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.

Aspects of elementary number theory illustrated in the spreadsheet environment

Number theory has in recent decades assumed a great practical importance, due primarily to its application to cryptography. This chapter discusses how elementary concepts of number theory may be illuminated and made accessible to upper secondary school students via appropriate spreadsheet models. In such environments, students can observe patterns, gain structural insight, form and test conjectures, and solve problems. The chapter begins by reviewing literature on the use of spreadsheets in general and the use of spreadsheets in number theory in particular. Two sample applications are then discussed. The first, factoring factorials, is presented and instructions are given to construct a model in Excel 2007. The second application, the RSA cryptosystem, is included because of its importance to Science, Technology, Engineering, and Mathematics (STEM) students. Number theoretic concepts relevant to RSA are discussed, and an outline of RSA. is given, with example. The chapter ends with instructions on how to construct a simple spreadsheet illustrating RSA.

Spreadsheet Conditional Formatting Illuminates Investigations into Modular Arithmetic

Modular arithmetic has often been regarded as something of a mathematical curiosity, at least by those unfamiliar with its importance to both abstract algebra and number theory, and with its numerous applications. However, with the ubiquity of fast digital computers, and the need for reliable digital security systems such as RSA, this important branch of mathematics is now considered essential knowledge for many professionals. Indeed, computer arithmetic itself is, ipso facto, modular. This chapter describes how the modern graphical spreadsheet may be used to clearly illustrate the basics of modular arithmetic, and to solve certain classes of problems. Students may then gain structural insight and the foundations laid for applications to such areas as hashing, random number generation, and public-key cryptography.

Raw data for project "Development of a DNA based aging technique for use in fisheries assessments" Fisheries and Development Corporation project 2007/033

The primary aim of this study was to determine the relationship between telomere length and age in a range of marine invertebrates including abalone (Haliotis spp) oysters (Saccostrea glomerata), spiny lobsters (Sagmariasus verreauxi formerly Jasus verreauxi and Jasus edwardsii) and school prawns (Metapenaeus macleayi). Additionally, this relationship was studied in a vertebrate organism using the freshwater fish Silver perch (Bidyanus bidyanus). Telomere length differences between tissues were also examined in some species such as Saccostrea glomerata, Sagmariasus verreauxi and Bidyanus bidyanus. In some cases cultured specimens of known age were used and this is quoted in the spreadsheets. For other wild-caught specimens where age was not known, size was used as a proxy for age. This may be a broad size class, or be determined by shell size or carapace length depending on the organism. Each spreadsheet contains raw data of telomere length estimates from Terminal Restriction Fragment Assays (TRF) for various individuals of each species including appropriate details such as age or size and tissue. Telomere length estimates are given in base pairs (bp). In most cases replicate experiments were conducted on groups of samples three times but on a small number of occasions only two replicate experiments were conducted. Further description of the samples can be found in final report of FRDC 2007/033. The arithmetic average for each individual (sample ID) across the two or three replicate experiments is also given. Bidyanus bidyanus (SilverPerch) Two sheets are contained within. a) Comparison of telomere length between different tissues (heart, liver and muscle) within the three year old age class - two replicate experiments were conducted. b) Comparison of telomere length between fish of different but known ages (0.25, 1, 2, and 3 years old) in each of three tissues, heart, liver and muscle – three replicate experiments were conducted per tissue. Haliotis spp (Abalone species) Three species were tested. H. asinina Telomere length was compared in two age classes-11 month and 18 month old abalone using muscle tissue from the foot. Within gel-variation was also estimated using a single sample run three times on one gel (replicate experiment). H. laevigata x H. rubra hybrids Telomere length was compared in three known age classes – two, three and four years old using muscle tissue from the foot. H. rubra Telomere length was compared in a range of different sized abalone using muscle tissue from the foot. Shell size is also given for each abalone Saccostrea glomerata Three sheets are contained within the file. a) Samples came from Moreton Bay Queensland in 2007. Telomere length was compared in two tissues (gill and mantle) of oysters in three age groups (1, 3 and 4 years) b) Samples came from Moreton Bay Queensland in 2009. Telomere length was compared in three age classes using DNA from gill tissue only c) Samples came from Wallis Lake, New South Wales. Telomere length was estimated from whole body minus the shell from 1 year old oysters, gill tissue of 3 age classes (1.5 years, 3 and 4 years), mantle tissue of two age classes (3 and 4 years). Sagmariasus verreauxi (formerly Jasus verreauxi) Telomere length was estimated from abdomen tissue of puerulus, gill and muscle tissue of 3 year old, large and very large size classes of lobsters. Jasus edwardsii Telomere length was measured in two size classes of lobsters- adults of varying sizes using muscle tissue and puerulus using tissues from the abdomen minus the exoskeleton. Metapenaeus macleayi Telomere length was measured in three size classes of school prawns adults. Muscle tissue was used, minus the exoskeleton.

Driving better vegetable irrigation through profitable practice change

The availability and quality of irrigation water has become an issue limiting productivity in many Australian vegetable regions. Production is also under competitive pressure from supply chain forces. Producers look to new technologies, including changing irrigation infrastructure, exploring new water sources, and more complex irrigation management, to survive these stresses. Often there is little objective information investigating which improvements could improve outcomes for vegetable producers, and external communities (e.g. meeting NRM targets). This has led to investment in inappropriate technologies, and costly repetition of errors, as business independently discover the worth of technologies by personal experience. In our project, we investigated technology improvements for vegetable irrigation. Through engagement with industry and other researchers, we identified technologies most applicable to growers, particularly those that addressed priority issues. We developed analytical tools for ‘what if’ scenario testing of technologies. We conducted nine detailed experiments in the Lockyer Valley and Riverina vegetable growing districts, as well as case studies on grower properties in southern Queensland. We investigated root zone monitoring tools (FullStop™ wetting front detectors and Soil Solution Extraction Tubes - SSET), drip system layout, fertigation equipment, and altering planting arrangements. Our project team developed and validated models for broccoli, sweet corn, green beans and lettuce, and spreadsheets for evaluating economic risks associated with new technologies. We presented project outcomes at over 100 extension events, including irrigation showcases, conferences, field days, farm walks and workshops. The FullStops™ were excellent for monitoring root zone conditions (EC, nitrate levels), and managing irrigation with poor quality water. They were easier to interpret than the SSET. The SSET were simpler to install, but required wet soil to be reliable. SSET were an option for monitoring deeper soil zones, unsuitable for FullStop™ installations. Because these root zone tools require expertise, and are labour intensive, we recommend they be used to address specific problems, or as a periodic auditing strategy, not for routine monitoring. In our research, we routinely found high residual N in horticultural soils, with subsequently little crop yield response to additional nitrogen fertiliser. With improved irrigation efficiency (and less leaching), it may be timely to re-examine nitrogen budgets and recommendations for vegetable crops. Where the drip irrigation tube was located close to the crop row (i.e. within 5-8 cm), management of irrigation was easier. It improved nitrogen uptake, water use efficiency, and reduced the risk of poor crop performance through moisture stress, particularly in the early crop establishment phases. Close proximity of the drip tube to the crop row gives the producer more options for managing salty water, and more flexibility in taking risks with forecast rain. In many vegetable crops, proximate drip systems may not be cost-effective. The next best alternative is to push crop rows closer to the drip tube (leading to an asymmetric row structure). The vegetable crop models are good at predicting crop phenology (development stages, time to harvest), input use (water, fertiliser), environmental impacts (nutrient, salt movement) and total yields. The two immediate applications for the models are understanding/predicting/manipulating harvest dates and nitrogen movements in vegetable cropping systems. From the economic tools, the major influences on accumulated profit are price and yield. In doing ‘what if’ analyses, it is very important to be as accurate as possible in ascertaining what the assumed yield and price ranges are. In most vegetable production systems, lowering the required inputs (e.g. irrigation requirement, fertiliser requirement) is unlikely to have a major influence on accumulated profit. However, if a resource is constraining (e.g. available irrigation water), it is usually most profitable to maximise return per unit of that resource.

Scientists in Control: a progressive approach to preparing work ready graduates in QC, EQA and method evaluation

Introduction QC, EQA and method evaluation are integral to delivery of quality patient results. To ensure QUT graduates have a solid grounding in these key areas of practice, a theory-to-practice approach is used to progressively develop and consolidate these skills. Methods Using a BCG assay for serum albumin, each student undertakes an eight week project analysing two levels of QC alongside ‘patient’ samples. Results are assessed using both single rules and Multirules. Concomitantly with the QC analyses, an EQA project is undertaken; students analyse two EQA samples, twice in the semester. Results are submitted using cloud software and data for the full ‘peer group’ returned to students in spreadsheets and incomplete Youden plots. Youden plots are completed with target values and calculated ALP values and analysed for ‘lab’ and method performance. The method has a low-level positive bias, which leads to the need to investigate an alternative method. Building directly on the EQA of the first project and using the scenario of a lab that services renal patients, students undertake a method validation comparing BCP and BCG assays in another eight-week project. Precision and patient comparison studies allow students to assess whether the BCP method addresses the proportional bias of the BCG method and overall is a ‘better’ alternative method for analysing serum albumin, accounting for pragmatic factors, such as cost, as well as performance characteristics. Results Students develop understanding of the purpose and importance of QC and EQA in delivering quality results, the need to optimise testing to deliver quality results and importantly, a working knowledge of the analyses that go into ensuring this quality. In parallel to developing these key workplace competencies, students become confident, competent practitioners, able to pipette accurately and precisely and organise themselves in a busy, time pressured work environment.

A preliminary investigation into technology and processes facilitating the assurance of learning

This paper reports on the outcomes from a preliminary evaluation of technologies and processes intended to support the Assurance of Learning initiative in the business faculty of an Australian university. The study investigated how existing institutional information systems and operational processes could be used to support direct measures of student learning and the attainment of intended learning goals. The levels at which learning outcomes had been attained were extracted from the University Learning Management System (LMS), based on rubric data for three assessments in two units. Spreadsheets were used to link rubric criteria to the learning goals associated with the assessments as identified in a previous curriculum mapping exercise, and to aggregate the outcomes. Recommendations arising from this preliminary study are made to inform a more comprehensive pilot based on this approach, and manage the quality of student learning experiences in the context of existing processes and reporting structures.

Redução do uso e do consumo de açúcar por merendeiras de escolas públicas : ensaio randomizado por conglomerado

O Brasil é um dos maiores consumidores per capita de açúcar e estudos têm mostrado um papel específico do consumo excessivo de açúcar no ganho de peso. Com o aumento do ganho de peso observado em vários países, e também no Brasil, é importante testar quais mensagens, estratégias e propostas de intervenção seriam eficazes na prevenção dessa epidemia. Os dados reportados são referentes a um ensaio randomizado por conglomerado, controlado, conduzido em 20 escolas municipais na cidade metropolitana de Niterói no Estado de Rio de Janeiro, de março a dezembro de 2007, que testou a eficácia de orientações para merendeiras objetivando reduzir a disponibilidade de açúcar e de alimentos fontes de açúcar na alimentação escolar e no consumo delas. A intervenção consistiu em um programa de educação nutricional nas escolas usando mensagens, atividades e material educativo que encorajassem a redução da adição de açúcar na alimentação escolar pelas merendeiras e no consumo delas. A redução da disponibilidade per capita de açúcar pelas escolas foi analisada através de planilhas com dados da utilização dos itens do estoque. O consumo individual das merendeiras foi avaliado através de questionário de freqüência de consumo alimentar. As medidas antropométricas e bioquímicas foram realizadas de acordo com técnicas padronizadas. As escolas de intervenção apresentaram maior redução da disponibilidade per capita de açúcar quando comparadas às escolas controle (-6,0 kg vs. 3,4 kg), mas sem diferença estatisticamente significante. Houve redução no consumo de doces e bebidas açucaradas nas merendeiras dos dois grupos, mas o consumo de açúcar não apresentou diferenças estatisticamente significativas entre eles. Houve redução do consumo de energia total nos dois grupos, mas sem diferença entre eles, e sem modificação dos percentuais de adequação dos macronutrientes em relação ao consumo de energia. Ao final do estudo somente as merendeiras do grupo de intervenção conseguiram manter a perda de peso, porém sem diferença estatisticamente significante. A estratégia de redução da disponibilidade e do consumo de açúcar por merendeiras de escolas públicas não atingiu o principal objetivo de redução de adição de açúcar. Uma análise secundária dos dados avaliou a associação entre a auto-percepção da saúde e da qualidade da alimentação com o excesso de peso e concentração elevada de colesterol sérico das merendeiras na linha de base. As perguntas de auto-percepção foram coletadas por entrevista. Dentre as que consideraram a sua alimentação como saudável, 40% apresentavam colesterol elevado e 61% apresentavam excesso de peso vs. 68% e 74%, respectivamente, para as que consideraram a sua alimentação como não-saudável. Dentre as que consideraram a sua saúde como boa, 41% apresentavam colesterol elevado e 59% apresentavam excesso de peso vs. 71% e 81%, respectivamente, para as que consideraram a sua saúde como ruim. A maioria das mulheres que relatou ter alimentação saudável apresentou maior frequência de consumo de frutas, verduras e legumes, feijão, leite e derivados e menor freqüência de consumo de refrigerante. Conclui-se que perguntas únicas e simples como as utilizadas para a auto-avaliação da saúde podem também ter importância na avaliação da alimentação.

A Low-level Geographic Information System for coastal zone management, with applications to Brunei Darussalam: Part I: The concept and its design elements

This contribution is the first part of a four-part series documenting the development of B:RUN, a software program which reads data for common spreadsheets and presents them as low-resolution maps of slates and processes. The program emerged from a need which arose during a project in Brunei Darussalam for a 'low level' approach for researchers to communicate findings as efficiently and expeditiously as possible. Part I provides a overview of the concept and design elements of B:RUN. Part II will highlight results of the economics components of the program evaluating different fishing regimes, sailing distances from ports and fleet operating costs. Environmental aspects will be presented in Part III in the form of overlay maps. Part IV will summarize the implications of B:RUN results to coastal and fishery resources management in Brunei Darussalam and show how this approach can be adapted to other coastlines and used as a teaching and training tool. The following three parts will be published in future editions of Naga, the ICLARM Quarterly. The program is available through ICLARM.

Beverton and Holt equations: spreadsheet functions and uncertainty

This contribution illustrates how modern spreadsheets aid the calculation and visualization of yield models and how the effects of uncertainties may be incorporated using Monte Carlo simulation. It is argued that analogous approaches can be implemented for other assessment models of simple to medium complexity justifying wider use of spreadsheets in fisheries analysis and training.